Newton polygons of higher order in algebraic number theory

Enric Nart; Jesús Montes; Jordi Guàrdia

doi:10.1090/S0002-9947-2011-05442-5

Newton polygons of higher order in algebraic number theory

Enric Nart, Jesús Montes, Jordi Guàrdia

Departament de Matemàtiques

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We develop a theory of arithmetic Newton polygons of higher order that provides the factorization of a separable polynomial over a p-adic field, together with relevant arithmetic information about the fields generated by the irreducible factors. This carries out a program suggested by Ø. Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number fields. © 2011 American Mathematical Society.

Idioma original	Anglès
Pàgines (de-a)	361-416
Revista	Transactions of the American Mathematical Society
Volum	364
Número	1
DOIs	https://doi.org/10.1090/S0002-9947-2011-05442-5
Estat de la publicació	Publicada - 1 de gen. 2012

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10.1090/S0002-9947-2011-05442-5

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AU - Guàrdia, Jordi

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AB - We develop a theory of arithmetic Newton polygons of higher order that provides the factorization of a separable polynomial over a p-adic field, together with relevant arithmetic information about the fields generated by the irreducible factors. This carries out a program suggested by Ø. Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number fields. © 2011 American Mathematical Society.

KW - Discriminant

KW - Newton polygon

KW - Integral basis

KW - Local field

KW - Prime ideal decomposition

KW - Number field

KW - P-adic factorization

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Newton polygons of higher order in algebraic number theory

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